Correcting Paintwork issue

[Sir Bagalot]

Lady B bought a used car a few months back. Transpires it's had paintwork at some point (possible chips away?)

The doors on one side feel as if they have over-spray along with half of one of the wings. When looked at at a certain angle also looks to have a boomerang shaped scratch painted in, and where it feels rough it looks dull.

I'm not after a full detail but I would like to get rid of the dullness and bring some shine to it.

Will a simple buffering do the job? And if so what's an average price I should be looking to pay?

[paintman]

Think you'll be better asking for recommendations local to you.
In view of what you've said it's going to need to be seen by someone that knows what they're about to decide the best course of action - whether that be a polishing or a respray.